All these 3 aspects are intertwined, but while Elune herself has been a mystery, the Order of Elune hasn't been expounded on. Suramar and the Cathedral of Eternal light should have really shown that side, but it was cut... dev panels showed us a glimpse of what they did, before revealing they cut it - and in 8.1, we get this other side of Elune hinted at in the 3 sisters encounter in the Cathedral of Eternal Night.
Anyway, I feel there is a lot to do with the stars and the night elves, that is more than just magic, but is very much related to magic, they have yet to people why all night elf disciplines use arcane star magic, how is this different form when mages use the well of eternity (i can think of a few easy explanations how - like they draw from the stars and moon instead of the well, and the mentality and use of the power is very different, they have spirituality to the arcane, whiles mages is more scientific/application wise, so the utilisation is different - priestess regard the well and arcane as very sacred (Elune's power), mages a tool - there was no conflict for a long time, because mages too took using that power very seriously too - this is how htey got to master it. It was only well after Azshara was established and after addiction had become problematic towards the end of the era, that they started being callous towards it. WoA remarks the night elves found it troubling how reckless the Highborne usage of the well was, and some Highborne too were very concerned, it also mentions that the night elves di not like this type of behaviour in general .. this supports my explanation. The way the sentinels and priests treat the Moonwells and the Well of Eternity confirms this also, WoW quests show them talking about it as the sacred waters of Elune -this is how they view the Well, so it would be very irksome what the Queen was doing, though it's the Highborne they felt were responsible for this (not the Queen).
Much supports this strong connections, not just the priestesses spells being arcane, but you see it time and time again, even in the ruins of Zin'Azshari, fighting some of the priests, like in that world boss encounter there, you see it also in the Cathedral of Eternal night, you saw it in Wc3 with starfall, etc) So I surmise it how they use the magic is different, I also suspect that the knowledge of the arcane came from the priests first, because Elune is worshipped before the mage order is created/rises to power, and they are the ones intensely studying the 'Well.
so it is priestly knowledge and the fruits it yields that causes others to start finding more applications for magic that are not necessarily faith centred, this is where magecraft is born, and this is where they divulge a bit, the priesthood continues in its foundation, bringing a level of spirituality to the race, but other things count. Nature is also not forgotten, love of nature is seen everywhere amongst every group, just the degree varies, highest amongst the forest dwellers, lowest amongst the Highborne.
I suspect it is their star fascination that leads them to discover how to draw arcane power from the stars and moon, but I suspect it influences far more than magic..also having spiritual and superstitious overtones... which blizzard yet have to show. Stars tell time, positions (portal magic comes form this, or should come from this), , they would tell destinies and futures via the stars, - so names would come form the stars, also it fits that their society would already pre-determine the future of the children by reading their stars guiding them a long a path. They would have a star name, a star stone/token, as well as a nature one. I would think while the cities are built on ley lines, the buildings would be aligned to the star patterns to maximise spell work in extraordinary ways.. there is a lot of depth you can bring out - all of this can stem from the priesthood and showing how it influences both the civilization, the source of the mage order as well as the druids and nature seeing Cenarius is Eluen's son.
Also Elune while the main goddess, is not the only celestial entity paid attention too, the stars would play a role hear, they probably view themselves as stars or the children of the stars that are Elune's (the moon, the great light's) , celestial court